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Proof step 6 from proof valid-global-sqn-write-valid (previous step)

apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # apebs, valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), n ≤ valid-sqns(v, m2, apebs).max, valid-sqns(v, m2, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]) ≠ ∅ → valid-sqns(v, m2, apebs[m, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)]).max < n ⊦ valid-sqns(v, m2, apebs) = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ n < # apebs → valid-sqns(v, m, apebs[n, apeb]) = (valid-sqns(v, m, apebs) \ (valid-peb(v, m, apebs[n]) ⊃ {apebs[n].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m, apeb) ⊃ {apeb.vidhdr.sqn} ;∅)
Proof step 8:
apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # apebs, valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), n ≤ valid-sqns(v, m2, apebs).max, (valid-sqns(v, m2, apebs) \ (valid-peb(v, m2, apebs[m]) ⊃ {apebs[m].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {mkpeb(aehdr, avhdr, buf1, m1, boolvar1).vidhdr.sqn} ;∅) ≠ ∅ → ( (valid-sqns(v, m2, apebs) \ (valid-peb(v, m2, apebs[m]) ⊃ {apebs[m].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {mkpeb(aehdr, avhdr, buf1, m1, boolvar1).vidhdr.sqn} ;∅) ).max < n ⊦ valid-sqns(v, m2, apebs) = ∅

Rule argument

spec: sqns name: valid-sqns-write seq: ⊦ n < # apebs → valid-sqns(v, m, apebs[n, apeb]) = ( valid-sqns(v, m, apebs) \ (valid-peb(v, m, apebs[n]) ⊃ {apebs[n].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m, apeb) ⊃ {apeb.vidhdr.sqn} ;∅) subst: [apeb, n, apebs, m, v] → [mkpeb(aehdr, avhdr, buf1, m1, boolvar1), m, apebs, m2, v] flags: <all paths>

Additional information

Used terms: mkpeb(aehdr, avhdr, buf1, m1, boolvar1), m, apebs, m2, v